According to the Swazi Observer, the Manzini Wanderers forward left Swaziland at the weekend to undergo a one-week assessment with Abafana Bes'thende.
Arrows freed up some foreign quota space with the recent departure of Zimbabwean attackers Kudakwashe Mahachi and Thomas Chideu.
Mahachi joined Soweto giants Orlando Pirates, while striker Chideu was released by the Durban-based outfit.
Dombo's manager Allan Kibangula confirmed his client is being assessed by Clinton Larsen's technical team.
"The player will start training with Arrows today after they showed interest to sign him," said Kibangula.
"I will be waiting for a report from Arrows before the end of the week and we will take it from there."
The Absa Premiership side have retained the services of proven marksman Lerato Lamola and Malawian defender Limbikani Mzava ahead of the new season.